World01 Wikia
Resource Séminaire Bourbaki: http://www.numdam.org/numdam-bin/browse?j=SB Séminaire Henri Cartan: http://www.numdam.org/numdam-bin/feuilleter?j=SHC The Feynman Lectures on Physics: http://www.feynmanlectures.caltech.edu/ Archive Inference: http://inference-review.com/ Numdam: http://www.numdam.org/ Mathdoc: http://www.mathdoc.fr/ Springer Link: http://link.springer.com/ Project Euclid: http://projecteuclid.org/ Göttinger Digitalisierungszentrum: http://gdz.sub.uni-goettingen.de/ Ian Bruce: http://www.17centurymaths.com/ History MacTutor History of Mathematics: http://www-history.mcs.st-and.ac.uk/ The History of Mathematics: http://www.maths.tcd.ie/pub/HistMath/ Historical Mathematics Collection: http://quod.lib.umich.edu/u/umhistmath/ Cornell University Mathematics Library: http://mathematics.library.cornell.edu/ Errata Selick: http://www.math.toronto.edu/selick/errata.txt Rotman: http://www.math.uiuc.edu/%7Erotman/errhomalg.pdf Exams http://papyrus.math.ucla.edu/gradquals/hbquals.php Seminar Ensifer like Seminar Bourbaki, introducing recent significant progess and trying to extend methods used and deepen results obtained and in the best case reveal a hidden structure and build a powerful general thoery out of these leading once again to the unification of all parts of Mathematics Mowing and Sowing A Scientific Biography of ALEXANDER GROTHENDIECK To the Reader Turn to the table of contents, follow the entries in italics, and you will find an almost entirely nonscientific biography of Grothendieck. Turn to the first chapter and you will find a nontechnical tour through this book, some personal reminiscences, and an attempt at a general assessment. The principal aim of this work is to present a scientific biography of Alexander Grothendieck. I shall attempt to sketch the concepts of the mathematical world as they were when Grothendieck became a mathematician, how he changed them, and what scientific inheritance he left. This book is an essay in open history, open because Grothendieck's oeuvre left us with unresolved questions of principle. The search for their answers is a central quest of mathematics today. Most issues cannot be discussed without entering into mathematical details, so I refer to my TM frequently (companion to Canons & Giants, which serves equally well for this pourpose). Each chapter has its own set of references, which are marked in the text by a square bracket containing a letter and a number. The following abbreviations have been used for entries that occur frequently: R&S: Récoltes et Semailles S-A: Serre-Grothendieck correspondence *Purpose and plan It is a great loss that when I decided to write a biography of Alexander Grothendieck when I was twenty years, He had already passed away; indeed only a few of his fellows were alive. When I truly began to write it, all of them also died. And I have no chance to talk to them ever. So is it appropriate for me to write a biography? Indeed even I talked some youger generation, such as Shela, my information is second-hand and there must be loss of credutiality. But I believe I can some how manage to avoid it; his works are all available to me and they reveal much more than one would expect. And I believe, I as a mathematician and as a spiritual pisple of Grothendieck, I can better understand his mathematical ideas, though not his political ones. After all I would write a scientific biography; my intended readers are working mathematicians and promising mathematical students, not ordinary people in general. I never avoid any mathematical details but I will explain all my terminology. I must admit that, I, as David Mumford, is a great admirer of Grothendieck. He is to me more important intelectually than any one in history. Despite his immediate fame in his lifetime , I don't think people have understood all of his vast legacy. So I followed his steps but at the same time, both as a inheriter and a explorer , tried to find new grand landscapes. That leads finally to the grand unification of topology and geometry algebraic in the 30's. *Algebraic geometry *A portrait of the mathematician as a young man *His parents and his *Functional Analysis *Homological Algebra *Algebraic Geometry *The political activities *Rupture and *Later life *Algebraic Geometry again *Journey's end *Appendices *Chronology *Index Tractatus Matheseos A companion to Canons & Giants. A mathematics treatise including not only fundamentals of all central mathematics branches but also most recent significant results and proofs (if they can be encompassed in the general theory) *Prologue *Main Body *Epilogue *Bibliography *Index *Special Part: Mathematical Models for Physical Phenomena studying all physical (natural) phenomena using mathematical methods and indicating where maths doesn't work physics and chemistry and biology Canons and Giants A work studying canons and giants in Mathematics including evaluation and commentary Archimedes *b. Syracuse, c. -287; d. Syracuse, -212. *DSB entry: http://www.encyclopedia.com/topic/Archimedes.aspx The first super-first-rate mathematician. Sir Isaac Newton *b. Woolsthorpe, England, 25 December 1642; d. London, England, 20 March 1727. *The Newton Project: http://www.newtonproject.sussex.ac.uk/prism.php?id=1 *DSB entry: http://www.encyclopedia.com/topic/Sir_Isaac_Newton.aspx The greatest physicist of all time, the second super-first-rate mathematician (after Arichimedes). Leonhard Euler *b. Basel, Switzerland, 15 April 1707; d. St. Petersburg, Russia, 18 September 1783. *The Euler Archive: http://eulerarchive.maa.org/ *DSB entry: http://www.encyclopedia.com/topic/Johann_Tobias_Mayer.aspx Joseph-Louis Lagrange *b. Turin, Italy, 25 January 1736; d Paris, France, 10 April 1813. *DSB entry: www.encyclopedia.com/topic/Joseph-Louis_Louis_Lagrange.aspx Carl Friedrich Gauss *b. Brunswick, Germany, 30 April 1777; d. Göttingen, Germany, 23 February 1855. *Werke: http://resolver.sub.uni-goettingen.de/purl?PPN235957348 *DSB entry: http://www.encyclopedia.com/topic/Carl_Friedrich_Gauss.aspx The third super-first-rate mathematician (after Achemedes and Newton). Évariste Galois *b. Bourg-la-Reine, France, 25 October 1811; d. Paris. 31 May 1832. *DSB entry: http://www.encyclopedia.com/topic/Evariste_Galois.aspx *''The mathematical writings of Évariste Galois'' **edited and translated by Peter Michael Neumann In this chapter we focus on Évariste Galois (1811-1832), whose originality in mathematics can be compared by no one before him (not even Newton and Gauss), and by only Riemann and Grothendieck after him. He is the mathematician who died most prematurely (20 years and five months). I cannot imagine what impact he would have on mathematics had he not died so early and his ideas been better understood by his contempararies; almost certainly it would be as great as that of Riemann (who may be properly considered to be the one whose influences are most profound and enduring). 1811.10.25 born Bourg-la-Reine, France Empire; Father: Nicolas-Gabriel Galois (1775-1829) Mother: Adelaide-Marie Demante (1788-1872) 1823 Fall 1831.5.9 1831.7.14 1832.5.30 1832.5.31 Bernhard Riemann *b. Breselenz, near Dannenberg, Germany, 17 September 1826; d. Selasca, Italy, 20 July 1866. *Gesammelte mathetmatische Werke und wissenschaftlicher Nachlass *DSB entry by Hans Freudenthal: http://www.encyclopedia.com/topic/Bernhard_Riemann.aspx The most influential mathematician of all time. Richard Dedekind *b. Brunswick, Germany, 6 October 1831; d. Brunswick, 12 February 1916. *Gesammelte mathematische Werke: http://resolver.sub.uni-goettingen.de/purl?PPN235685380 *DSB entry: http://www.encyclopedia.com/doc/1G2-2830901117.html Georg Cantor *b. St. Petersburg, Russia, 3 March 1845; d. Halle, Germany, 6 January 1918. *Gesammelte Abhandlungen: http://resolver.sub.uni-goettingen.de/purl?PPN237853094 *DSB entry: http://www.encyclopedia.com/topic/Georg_Cantor.aspx Felix Klein *b. Düsseldorf, Germany, 25 April 1849; d. Göttingen, Germany, 22 June 1925. *Gesammelte mathematische Abhandlungen: http://resolver.sub.uni-goettingen.de/purl?PPN237839962 *DSB entry: http://www.encyclopedia.com/topic/Felix_Klein.aspx Henri Poincaré *b. Nancy, France, 29 April 1854; d. Paris, France, 17 July 1912. *Archives Henri Poincaré: http://henripoincarepapers.univ-lorraine.fr/ *DSB entry by Jean Dieudonné: http://www.encyclopedia.com/topic/Jules_Henri_Poincare.aspx David Hilbert *b. Königsberg, Germany, 23 January 1862; d. Göttingen, Germany, 14 February 1943. *Gesammelte Abhandlungen: http://resolver.sub.uni-goettingen.de/purl?PPN237820250 *DSB entry by Hans Freudenthal: http://www.encyclopedia.com/topic/David_Hilbert.aspx Élie Cartan *b. Dolomieu, France, 9 April 1869; d. Paris, France, 6 May 1951. *Oeuvres complètes *DSB entry by Jean Dieudonné: http://www.encyclopedia.com/doc/1G2-2830900800.html Alexander Grothendieck *b. Berlin, Germany, 28 March 1928; d. Saint-Girons, France, 13 November 2014. *The Grothendieck Circle: http://www.grothendieckcircle.org/ *''Récoltes et Semailles'' **partial English translation by Roy Lisker: http://www.fermentmagazine.org/rands/recoltes1.html My intellectual mentor; the one who brought most new concepts in history and had a style all his own. Michael Atiyah *b. London, England, 22 April 1929; David Mumford *b. Worth, England, 11 June 1937; *Archive: http://www.dam.brown.edu/people/mumford/ Pierre Deligne *b. Etterbeek, Belgium, 3 October 1944; Alain Connes *b. Draguignan, France, 1 April 1947; Andrew Wiles *b. Cambridge, England, 11 April 1953; A good story in mathematics. Grigori Perelman *b. Leningrad, Russia, 13 June 1966; Euclid Archimedes Viete Descartes Italian algebraists (imagery number) Cayley